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COMP LAB
G. Mallia
Timetable
Deadline
Aims
Systems
Vibrations
How
Simulation
types
Classical
simulation
First step
How to write
a report
INTRODUCTIONto the Computational Laboratory
Giuseppe Malliag.mallia@imperial.ac.uk
Imperial College London - Chemistry Department
Thomas Young Centre:
the London Centre for Theory and Simulation of Materials
1 February 2010 – 8 March 2010
COMP LAB
G. Mallia
Timetable
Deadline
Aims
Systems
Vibrations
How
Simulation
types
Classical
simulation
First step
How to write
a report
Outline
1 TIMETABLE and DEADLINE
2 AIMS and SYSTEMS
3 VIBRATIONS
4 HOW
5 SIMULATION TYPES
6 CLASSICAL SIMULATION
7 FIRST STEP
8 HOW TO WRITE A REPORT
COMP LAB
G. Mallia
Timetable
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TIMETABLE and DEADLINE → GROUP A
Statistical Mechanics: The Thermal Expansion of MgOMon Tue Thur Fri
2:00-5:00 08/03/10 09/03/10 11/03/10 12/03/10
COMP LAB
G. Mallia
Timetable
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Systems
Vibrations
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Simulation
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TIMETABLE and DEADLINE → GROUP A
Statistical Mechanics: The Thermal Expansion of MgOMon Tue Thur Fri
2:00-5:00 08/03/10 09/03/10 11/03/10 12/03/10
DEADLINE:
when? 13:00pm on Wed the 17th of Marchwhere? ROOM 442 to Ms Lisa Benbow
COMP LAB
G. Mallia
Timetable
Deadline
Aims
Systems
Vibrations
How
Simulation
types
Classical
simulation
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a report
TIMETABLE and DEADLINE → GROUP B
Statistical Mechanics: The Thermal Expansion of MgOMon Tue Thur Fri
2:00-5:00 01/02/10 02/02/10 04/02/10 05/02/10
COMP LAB
G. Mallia
Timetable
Deadline
Aims
Systems
Vibrations
How
Simulation
types
Classical
simulation
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How to write
a report
TIMETABLE and DEADLINE → GROUP B
Statistical Mechanics: The Thermal Expansion of MgOMon Tue Thur Fri
2:00-5:00 01/02/10 02/02/10 04/02/10 05/02/10
DEADLINE:
when? 13:00pm on Wed the 10th of Februarywhere? ROOM 442 to Ms Lisa Benbow
COMP LAB
G. Mallia
Timetable
Deadline
Aims
Systems
Vibrations
How
Simulation
types
Classical
simulation
First step
How to write
a report
AIM:
The Thermal Expansion of MgO
to predict how the material expands when heated;
to calculate the thermal expansion coefficient:α = 1
V0
(
∂V∂T
)
P
COMP LAB
G. Mallia
Timetable
Deadline
Aims
Systems
Vibrations
How
Simulation
types
Classical
simulation
First step
How to write
a report
AIM:
The Thermal Expansion of MgO
to predict how the material expands when heated;
to calculate the thermal expansion coefficient:α = 1
V0
(
∂V∂T
)
P
QUASI-HARMONIC APPROXIMATION (LD)to compute vibrational energy levels of MgO;to understand the phonon dispersion of a material andthe vibrational density of state;
COMP LAB
G. Mallia
Timetable
Deadline
Aims
Systems
Vibrations
How
Simulation
types
Classical
simulation
First step
How to write
a report
AIM:
The Thermal Expansion of MgO
to predict how the material expands when heated;
to calculate the thermal expansion coefficient:α = 1
V0
(
∂V∂T
)
P
QUASI-HARMONIC APPROXIMATION (LD)to compute vibrational energy levels of MgO;to understand the phonon dispersion of a material andthe vibrational density of state;
MOLECULAR DYNAMICS (MD)to simulate the vibrations as random motions of atomsinside a cell;
COMP LAB
G. Mallia
Timetable
Deadline
Aims
Systems
Vibrations
How
Simulation
types
Classical
simulation
First step
How to write
a report
AIM:
The Thermal Expansion of MgO
to predict how the material expands when heated;
to calculate the thermal expansion coefficient:α = 1
V0
(
∂V∂T
)
P
QUASI-HARMONIC APPROXIMATION (LD)to compute vibrational energy levels of MgO;to understand the phonon dispersion of a material andthe vibrational density of state;
MOLECULAR DYNAMICS (MD)to simulate the vibrations as random motions of atomsinside a cell;
to compare QUASI-HARMONIC APPROXIMATION withMOLECULAR DYNAMICS results.
COMP LAB
G. Mallia
Timetable
Deadline
Aims
Systems
Vibrations
How
Simulation
types
Classical
simulation
First step
How to write
a report
SYSTEMS: MgO crystal (fcc)
IDEAL, NON DEFECTIVE, PERIODIC SYSTEM IN 3D
CONVENTIONAL CELLac=bc=cc ; αc , βc , γc
Nc : number of atomsVc : volume
COMP LAB
G. Mallia
Timetable
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Systems
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Simulation
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simulation
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SYSTEMS: MgO crystal (fcc)
IDEAL, NON DEFECTIVE, PERIODIC SYSTEM IN 3D
CONVENTIONAL CELLac=bc=cc ; αc , βc , γc
Nc : number of atomsVc : volume
PRIMITIVE CELLap=bp=cp; αp, βp, γp
Nc : number of atomsVp: volume
COMP LAB
G. Mallia
Timetable
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Systems
Vibrations
How
Simulation
types
Classical
simulation
First step
How to write
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SYSTEMS: MgO crystal (fcc)
IDEAL, NON DEFECTIVE, PERIODIC SYSTEM IN 3D
CONVENTIONAL CELLac=bc=cc ; αc , βc , γc
Nc : number of atomsVc : volume
PRIMITIVE CELLap=bp=cp; αp, βp, γp
Nc : number of atomsVp: volume
SUPERCELLas=bs=cs= 2 × ac
αs , βs , γs
Ns : number of atomsVs : volume
COMP LAB
G. Mallia
Timetable
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Systems
Vibrations
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Simulation
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SYSTEMS II: lattice parameter of MgO
What is the lattice parameter of MgO?
COMP LAB
G. Mallia
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SYSTEMS II: lattice parameter of MgO
What is the lattice parameter of MgO?
CONVENTIONAL CELL
ac=bc=cc ; αc , βc , γc
COMP LAB
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SYSTEMS II: lattice parameter of MgO
What is the lattice parameter of MgO?
CONVENTIONAL CELL
ac=bc=cc ; αc , βc , γc
ac
COMP LAB
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SYSTEMS III
Is it possible to move
from the CONVENTIONAL CELL
to the PRIMITIVE CELL?
COMP LAB
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SYSTEMS III
Is it possible to move
from the CONVENTIONAL CELL
to the PRIMITIVE CELL?
COMP LAB
G. Mallia
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VIBRATIONS
COMP LAB
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VIBRATIONS:
WHY ARE THEY IMPORTANT? 1
Atoms vibrate around their equilibrium positions.
thermal properties: heat capacity, expansion
phase transitions, including melting
transport: thermal conductivity, sound
electrical properties, e.g., superconductivity
dielectric phenomena at low frequencies
1From Prof N. M. Harrison’s Lectrure Notes: Vibrations in crystals
COMP LAB
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VIBRATIONS: FROM A FINITE SYSTEM
TO AN INFINITE SYSTEM 1
1From Prof N. M. Harrison’s Lectrure Notes: Vibrations in crystals
COMP LAB
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VIBRATIONS:
WAVELENGTH - WAVEVECTOR 1
k =2π
λ
In this case, as k increases, the energy of vibration increasesand the frequency too.
1From Prof N. M. Harrison’s Lectrure Notes: Vibrations in crystals
COMP LAB
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VIBRATIONS:
PHONON DISPERSION 1
VIBRATIONAL FREQUENCY ω AS A FUNCTION OF k
1From Prof N. M. Harrison’s Lectrure Notes: Vibrations in crystals
COMP LAB
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VIBRATIONS:
PHONON DISPERSION 1
VIBRATIONAL FREQUENCY ω AS A FUNCTION OF k
SIMILARLY, ELECTRONIC BAND STRUCTURE OF THEHYDROGEN POLYMER
1From Prof N. M. Harrison’s Lectrure Notes: Vibrations in crystals
COMP LAB
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VIBRATIONS:
PHONON?
electron: WAVE or PARTICLE
radiation: WAVE or PARTICLE
COMP LAB
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VIBRATIONS:
PHONON?
electron: WAVE or PARTICLE
radiation: WAVE or PARTICLE (photon)
COMP LAB
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VIBRATIONS:
PHONON?
electron: WAVE or PARTICLE
radiation: WAVE or PARTICLE (photon)
vibration: WAVE or PARTICLE
COMP LAB
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VIBRATIONS:
PHONON?
electron: WAVE or PARTICLE
radiation: WAVE or PARTICLE (photon)
vibration: WAVE or PARTICLE (phonon)
COMP LAB
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VIBRATIONS:
1D MONOATOMIC CHAIN (OR POLYMER) 1
INFINITE NUMBER OF VIBRATIONS → BRANCH
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VIBRATIONS:
1D MONOATOMIC CHAIN (OR POLYMER) 1
INFINITE NUMBER OF VIBRATIONS → BRANCH
ωk =
√
4J
M|sin(ka/2)|
COMP LAB
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VIBRATIONS:
1D MONOATOMIC CHAIN (OR POLYMER) 1
INFINITE NUMBER OF VIBRATIONS → BRANCH
ωk =
√
4J
M|sin(ka/2)|
COMP LAB
G. Mallia
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VIBRATIONS:
DIRECT AND RECIPROCAL SPACE
1 PERIODIC DIRECTION IN THE
DIRECT SPACE!
a
1 PERIODIC DIRECTION IN THE
RECIPROCAL SPACE!
a∗ = 2πa
COMP LAB
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VIBRATIONS:
1D DIATOMIC CHAIN
(SIMILARLY TO THE POLYMER WITH H2 PER CELL)
FOLDING PROCESS!!!
COMP LAB
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VIBRATIONS:
1D HETERO DIATOMIC CHAIN 1
1From Prof N. M. Harrison’s Lectrure Notes: Vibrations in crystals
COMP LAB
G. Mallia
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VIBRATIONS:
OPTIC AND ACOUSTIC MODES
OPTIC:1) has a frequency that is in the vicinity of the optical region ofthe electromagnentic spectrum2) the atomic motions associated are the same as the responseto an oscillating electromagnentic field
ACOUSTIOC:1) has acoustic frequency
COMP LAB
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VIBRATIONS:
LONGITUDINAL AND TRANSVERSE MODES 1
1From Prof N. M. Harrison’s Lectrure Notes: Vibrations in crystals
COMP LAB
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VIBRATIONS:
3D HETERO DIATOMIC CRYSTAL 1
Neutron data for GaAs
1From Prof N. M. Harrison’s Lectrure Notes: Vibrations in crystals
COMP LAB
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HOW?
COMPUTATIONAL EXPERIMENT / SIMULATION
program
input
Environment:the choice of the Operating System → linux
Interface:DLV = package for the visualisation of materialsstructures and properties.
COMP LAB
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SIMULATION TYPES
CLASSICAL SIMULATION
Newton law → GULPQUANTUM-MECHANICAL SIMULATION
Schroedinger equation → CRYSTAL
Systems under investigation
Properties
Accuracy
Computational time
Resources
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CLASSICAL SIMULATION
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INTERATOMIC POTENTIAL
coulombic interaction
short term repusilve contribution
Morse-like potential
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QUASI-HARMONIC APPROXIMATION 1
HELMHOLTZ FREEENERGY
1From Prof N. M. Harrison’s Lectrure Notes: Vibrations in crystals
COMP LAB
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QUASI-HARMONIC APPROXIMATION I
HELMHOLTZ FREEENERGY
F = E − TS
F = F (T , V )
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MOLECULAR DYNAMICS 1
Initial configuration and initial velocities:the initial configuration will be that of ideal MgOthe velocities will be random but scaled to produceroughly the target temperature.
Compute the forces on the atoms (F).
Compute the accelerations a=F/m
Update the velocities: Vnew = Vold + a * dt
Update the positions of the atoms: Rnew = Rold + Vnew* dt
Repeat until average properties like E and T settle down
Once settled measure some properties.
1From Prof N. M. Harrison’s Lectrure Notes: Vibrations in crystals
COMP LAB
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GEOMETRY OPTIMIZATION I
What does it mean?
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GEOMETRY OPTIMIZATION I
What does it mean?
Minimization of the energy as a function
of the atomic position
(xi , yi , zi , with i = 1, N ,
and N is the number of atoms)
and of the lattice parameters
(a,b,c,α,β,γ)
COMP LAB
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GEOMETRY OPTIMIZATION II
How many variables for MgO?
COMP LAB
G. Mallia
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FIRST STEP
1 Restart the PCs that are running Windows;
2 Once you have a black screen with the following line:> boot:Type linux> boot: linuxPress Enter
3 Use your login and passwd as in Window
4 Open firefox: the web browser
5 http://www.ch.ic.ac.uk/harrison/Teaching/teaching.html
COMP LAB
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HOW TO WRITE A REPORT I
by Giulia C. De Fusco
Introduction
the system
the methodology (theory in use)
the aims of the exercise
the tools in use (programs)
Body of the text
write it like a scientific paper (well-articulated sentences,NOT a list of two-word answers)
analyse critically obtained data and given answers
round numerical answers to a specific number of decimalplaces (i.e. 4)
add literature/web citations whenever a comparison withexperimental data is required
add explicitely every formula used one to obtain results
check spelling
COMP LAB
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HOW TO WRITE A REPORT II
by Giulia C. De Fusco
Pictures
max 20
reasonably sized (NOT one-page sized pictures, but stillreadable)
white background (follow the instructions given on thewebsite clicking on the link ’How to save a picture for yourreport’)
described in caption or in the text
Graphs
add labels and units
add a critical comment whenever required (NOT a merelydescriptive comment)
COMP LAB
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HOW TO WRITE A REPORT III
by Giulia C. De Fusco
Tables
add labels and units
round numerical answers to a specific number of decimalplaces (i.e. 4)
repeat heading if the table cannot fit in a single page
Conclusions
give a general description of your calculations and yourmain findings
outline the differences between the methods in use and theresults obtained
analyse critically these differences
COMP LAB
G. Mallia
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THANK YOU!!!
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